Related papers: Sparse domination for rough multilinear singular i…

In this paper, we prove bilinear sparse domination bounds for a wide class of Fourier integral operators of general rank, as well as oscillatory integral operators associated to H\"ormander symbol classes $S^m_{\rho,\delta}$ for all…

In this paper, we will give the weighted bounds for multilinear fractional maximal type operators $\mathcal{M}_{\Omega,\alpha}$ with rough homogeneous kernels. We obtain a mixed $A_{(\vec{P},q)}-A_\infty$ bound and a $A_{\vec{P}}$ type…

Let $T_\Omega$ be the singular integral operator with variable kernel $\Omega(x,z)$. In this paper, by using the atomic decomposition theory of weighted weak Hardy spaces, we will obtain the boundedness properties of $T_\Omega$ on these…

In this paper we study integral operators with kernels \begin{equation*} K(x,y)= k_1( x- A_1y)...k_m( x-A_my), \end{equation*} $k_i(x)=\frac{\Omega_i(x)}{|x|^{n/q_i}}$ where $\Omega_i: \mathbb{R}^n\to \mathbb{R}$ are homogeneous functions…

This paper introduces and studies a class of multilinear fractional bounded mean oscillation operators (denoted {\rm $m$-FBMOOs}) defined on ball-basis measure spaces $(X, \mu, \mathcal{B})$. These operators serve as a generalization of…

Let $0<\alpha<n$ and $T_{\Omega,\alpha}$ be the homogeneous fractional integral operator which is defined by \begin{equation*} T_{\Omega,\alpha}f(x):=\int_{\mathbb R^n}\frac{\Omega(x-y)}{|x-y|^{n-\alpha}}f(y)\,dy, \end{equation*} where…

For any $0<\alpha<n$, the homogeneous fractional integral operator $T_{\Omega,\alpha}$ is defined by \begin{equation*} T_{\Omega,\alpha}f(x)=\int_{\mathbb R^n}\frac{\Omega(x-y)}{|x-y|^{n-\alpha}}f(y)\,dy. \end{equation*} In this paper, we…

We study the rough bilinear singular integral, introduced by Coifman and Meyer , $$ T_\Omega(f,g)(x)=p.v. \! \int_{\mathbb R^{n}}\! \int_{\mathbb R^{n}}\! |(y,z)|^{-2n} \Omega((y,z)/|(y,z)|)f(x-y)g(x-z) dydz, $$ when $\Omega $ is a function…

Let $T_{\Omega,\alpha}$ be the homogeneous fractional integral operator defined as \begin{equation*} T_{\Omega,\alpha}f(x):=\int_{\mathbb R^n}\frac{\Omega(x-y)}{|x-y|^{n-\alpha}}f(y)\,dy, \end{equation*} and the related fractional maximal…

We show that the $L^2(w)$ operator norm of the composition $M\!\circ T_{\Omega}$, where $M$ is the maximal operator and $T_{\Omega}$ is a rough homogeneous singular integral with angular part $\Omega\in L^{\infty}(S^{n-1})$, depends…

In the paper, we provide a new method to study the oscillatory singular integral operator $T_{Q,A}$ with nonstandard kernel defined by \[T_{Q,A} f(x)=\text { p.v. } \int_{\mathbb{R}^{n}} f(y)…

We establish the full quasi-Banach range of $L^{p_1}(\mathbb R) \times L^{p_2}(\mathbb R) \rightarrow L^p(\mathbb R)$ bounds for one-dimensional bilinear singular integral operators with homogeneous kernels whose restriction $\Omega$ to the…

Let $ T_{P } f (x) = \int e ^{i P (y)} K (y) f (x-y) \; dy $, where $ K (y)$ is a smooth Calder\'on-Zygmund kernel on $ \mathbb R ^{n}$, and $ P$ be a polynomial. We show that there is a sparse bound for the bilinear form $ \langle T_P f, g…

In this note, we show that if $T$ is a Calder\'on--Zygmund operator satisfying $T(1)=0$, then the usual sparse domination for $T$ can be sharpened by replacing local averages by local mean oscillations. As an application, we characterize…

Let $\Omega\in L^1{({\mathbb S^{n-1}})}$, be a function of homogeneous of degree zero, and $M_\Omega$ be the Hardy-Littlewood maximal operator associated with $\Omega$ defined by $M_\Omega(f)(x) =…

We prove that scalar-valued sparse domination of a multilinear operator implies vector-valued sparse domination for tuples of quasi-Banach function spaces, for which we introduce a multilinear analogue of the UMD condition. This condition…

We establish analogs of sharp weighted weak-type bounds for $m$-sublinear operators satisfying sparse form domination, including multilinear Calder\'on-Zygmund singular integrals. Our results, which hold for general $\vec{p} \in…

We establish the condition $(\Omega)$ for smooth kernels of various types of convolution and differential operators. By the $(DN)$-$(\Omega)$ splitting theorem of Vogt and Wagner, this implies that these operators are surjective on the…

We obtain an alternative approach to recent results by M. Lacey \cite{La} and T. Hyt\"onen {\it et al.} \cite{HRT} about a pointwise domination of $\omega$-Calder\'on-Zygmund operators by sparse operators. This approach is rather elementary…

This paper refines the main results from our previous study on sparse bounds of generalized commutators of multilinear fractional singular integral operators in \cite{CenSong2412}. The key improvements are: 1. We replace pointwise…